Reprojecting lyr file of Tiled Internet Layer created in ArcGIS Online?

Reprojecting lyr file of Tiled Internet Layer created in ArcGIS Online?

I have an ArcGIS lyr file describing Tiled Internet Layer (according to Data Source tab in properties).
This file was created in ArcGIS Online by defining a new tile layer and downloading it.
Everything is OK with it except the projection. ArcGIS Online sets the projection of any newly created layer as WGS_1984_Web_Mercator_Auxiliary_Sphere which is not correct in this case.
I need to change it to a proper one.
What i've already tried:

Change projection by redefining it via toolbox (Data Management ->
Define Projection. This gave me an error in ArcMap.
Rough text edit of lyr file (by replacing a WKT-string with projection definition). This gave me an error when I'd tried to add it to a MXD (something like "Adding the selected layer file failed. Maybe it was created using a newer version of ArcGIS" which is not true)
Change projection in ArcGIS Online

Is there any way to change the projection of such layer?

Solutions/Answers:

Answer 1:

In arcmap, Use define projection tool in data management tools to define the projection of the the tiles as WGS_1984_Web_Mercator_Auxiliary_Sphere. Once that is done, use the Project tool to re-project them the projection you need. Note that the projection mention in the layer properties is not an actual projection as lyr files cannot be projected but a description of the projection used for the data within that layer. You can manually change the description to suite your use.

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